Count By Tens and Hundreds Student Probe Sarah had 70 stickers. Then she got 30 more stickers. How many stickers does Lesson Description This lesson helps students develop an understanding of counting by tens and hundreds. They will read and write numerals and represent a number of objects with a written numeral. Rationale Early elementary students count and are exposed to patterns in numbers up to 1000. They begin to describe groups of ten and groups of a hundred as units. This provides a conceptual framework for understanding the base ten number system. Preparation Base ten blocks and hundred number charts should be available for students. At a Glance What: Counting equal groups in sets by tens and hundreds Common Core Standard: CC.1.NBT.5. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. Mathematical Practices: Make sense of problems and persevere in solving them. Model with mathematics. Use appropriate tools strategically. Who: Students who do not understand skip counting sets of equal groups. Grade Level: 2 Prerequisite Vocabulary: equal groups, ones, tens, hundreds Prerequisite Skills: count by ones to form equal groups connected to problems. Delivery Format: Individual or small group. Lesson Length: 15 to 30 min. Materials, Resources, Technology: Base ten blocks, hundreds number charts Student Worksheets: None Lesson The Expect students to say or do If students do not, then the 1. Sarah had 70 stickers. Then she got 30 more stickers. How many stickers does 70, 80, 90, 100 Represent each part of the problem. 2. Count the number of stickers Sarah has. 3. How many stickers did Sarah have to start with? 70, 80, 90, 100 Refer to Base Ten Representation Grouped Models 70 Use base ten blocks to show 70.
The Expect students to say or do If students do not, then the 4. Which blocks did you use? 10 rods When you use ones cubes it takes a long time to count. Is there a faster way to show 70? What if you use ten rods? 5. What will it sound like if you count ten rods? 6. How many ones are on your second ten rod? 7. How many numbers/spaces are on the second line of the hundreds number chart? 8. How many is two rows of ten numbers? 9. Can you count these rows by tens? 10. Can you count by tens to 70? 10, 20, 30, 40, 50, 60, 70 Let s compare your ten rods to the hundreds number chart. If there are 10 ones on this 10 rod, then it is the same as the first row on the hundreds number chart. Ten on the first row. 10 Count the blocks (spaces) on your ten rod. There are ten ones on the ten rod. 10 Count the numbers/spaces on the second row of the hundreds number chart. There are ten numbers on the second row. 20 Look at the hundreds number chart. Ten is at the end of the first row and twenty is at the end of the second row. Therefore, two rows of ten is twenty. 10, 20 You will only need to count the numbers at the end of each row in order to count by tens because there are ten numbers in each row. 10, 20, 30, 40, 50, 60, 70 There are ten numbers (or spaces) in each row on the hundreds number chart. Just like 10 is at the end of the first row and 20 is at the end of the second row, then 30 is at the end of the third row, 40 is at the end of the forth row, etc
The Expect students to say or do If students do not, then the 11. Are your ten rods the same as the rows on the hundred number chart? Yes Because you told me that there are ten ones on the ten rod and ten numbers on each line of the hundreds number chart, then the tens rods are the same as the two rows on 12. Count the tens rods you are using to show the 70 stickers Sarah had to begin with. 13. Sarah had 70 stickers. Then she got 30 more stickers. How many more stickers did Sarah get? 14. Now, show the 30 more stickers that Sarah got. 15. How will you count your ten rods that show 30? the hundreds number chart. 10, 20, 30, 40, 50, 60, 70 Use the hundreds number chart to count by tens to represent the 70 stickers Sarah had. 30 Follow the language of the problem. Sarah had 70 stickers. Then she got 30 more stickers. Students use ten rods to represent 30. If you use ones cubes, then it will take a long time. Can you use your ten rods like you did to show 70? 10, 20, 30 Remember that your ten rods are the same as each line on the hundreds number chart. You will count by tens. What will that sound like? 10,20,30
The Expect students to say or do If students do not, then the 16. Now that you have each part of the problem represented, let s reread the problem. Sarah had 70 stickers. Then she got 30 more stickers. How many stickers does Sarah have now? What should you do with each part? How many stickers does Join them together. 100 Sarah had 70 stickers. When the problem said that she got 30 more stickers, we know that the parts have to be put together. There is an action in the problem. Sarah got 30 more stickers. When you used ten rods to represent 70, you said 10, 20, 30, 40, 50, 60, 70. When you used ten rods to represent 30, you said 10, 20, 30. 17. How were you counting? By tens When you count ten rods you should count by tens. Remember, each ten rod is like each line on the hundreds number chart. 18. If you join each group together, you will join 70 and 30. Can you join your ten rods together to find out how many stickers Sarah has now? Student puts each group of ten rods together. Show me your group of ten rods that represents Sarah s 70 stickers. Now show me your group of ten rods that represents the 30 more stickers Sarah got. In order to find out how many stickers Sarah has now, you must join your groups together.
The Expect students to say or do If students do not, then the 19. How will you count the ten rods you joined together? By tens 20. What does it sound like when you join Sarah s 70 stickers and the 30 more stickers she got? 21. Write a number sentence to represents this problem. 22. What did you do with Sarah s 70 stickers and the 30 more she got? 23. What symbol will you use to show that you joined 70 and 30? 10,20,30,40,50,60,70, 80, 90, 100 Because you used ten rods you will count by tens. Remember, each ten rod is like each line on the hundreds number chart. Put one ten rod on each line of the hundreds number chart. Now use the hundreds number chart to help you count by tens. 70 + 30 = 100 How many stickers did Sarah have to begin with? 70 Record 70 on your paper. How many more stickers did Sarah get? 30 Record 30 next to 70. Put them together Because Sarah already had 70 and then she got 30 more stickers we know that she must join them together. Plus sign (+) The plus sign (+) is the symbol that means join together. Put the plus symbol between the 70 and 30. Now your number sentence says 70 joined with 30.
The Expect students to say or do If students do not, then the 24. How many stickers does 100 Remember how you joined 70 and 30. You counted by tens. Let s count your ten rods again. 10,20,30,40,50,60,70, 25. Where will you record 100? 26. What symbol should be between 70+30 and 100? 27. What will your number sentence look like for this problem? Teacher Notes None 80, 90, 100 After 70+30 Record 100 after 70 +30. 70 joined with 30 is the same as 100. The equals sign Because 70 + 30 is the same as 100, you will use the equals symbol. The equals symbol means the same as. 70 + 30 is the same as 100. 70 + 30 = 100 Seventy joined with 30 is represented by recording 70 + 30. This means that Sarah had 70 stickers and then she got 30 more stickers. 70 + 30 = 100 This means that 70 + 30 is the same as 100. Now Sarah has 100 stickers. Variations Sarah had 100 stickers. Then she gave 30 stickers to Ethan. How many stickers does Sarah have now?
Formative Assessment 1. Sarah had 60 stickers. Then she got 40 more stickers. How many stickers does Sarah have now? Show your work. 2. Sarah had 1000 stickers. Then she gave 400 stickers to Ethan. How many stickers does Show your work. References Thomas P. Carpenter, Elizabeth Fennema, Megan Loef Franke, Linda Levi, Susan B. Empson (1999). Children s Mathematics Cognitively Guided Instruction, Heinemann: Portsmouth, NH Van de Walle, John A., Karp, Karen S., and Bay-Williams, Jennifer M. (2010). Elementary and Middle School Mathematics Teaching Developmentally, Boston: Allyn & Bacon. Mathematics Preparation for Algebra. (n.d.). Retrieved May 12, 2011, from Doing What Works